Threaded connection with improved root thread profile

ABSTRACT

A threaded connection design having a double ellipse in the thread root for reducing stress fatigue is illustrated in this disclosure. The root groove includes a first portion comprising a first elliptical surface being part of a first ellipse. The root groove further includes a second portion comprising a second elliptical surface, being part of a second ellipse, and the second elliptical surface being joined tangentially at a first end to the first elliptical surface at a junction point that defines the bottom of the root groove. The second elliptical surface is joined tangentially at a second end to the load flank.

This application is a Divisional of and claims the benefit of priorityto U.S. patent application Ser. No. 13/315,354, filed on Dec. 9, 2011and entitled “Threaded Connection with Improved Root Thread Profile”,the contents of which are hereby incorporated by reference.

FIELD OF INVENTION

This invention relates in general to pipe connections, and in particularto a threaded connection having an improved root thread profile designthat improves fatigue resistance.

BACKGROUND

Searching for oil or more generally hydrocarbons is becoming moredemanding in terms of hardware and devices in recent years because oiland gas fields (reservoirs) are located deeper in the earth or in placesdifficult to reach.

Numerous onshore drilling and production activities require tubularconnections having high levels of fatigue resistance; for example,drilling applications and thermal applications.

Additionally, exploring and producing hydrocarbon fields in deep waterenvironments (offshore applications) has increased and necessitatestubular connections which are more resistant to environmental challengessuch as fatigue and corrosion.

Off-shore platforms have production facilities located above the seasurface. These facilities are frequently used for exploitation ofhydrocarbon fields lying below the sea floor. These platforms areanchored to the sea bottom and tubular strings are used to deliver thehydrocarbons from wells drilled into reservoirs below the sea bed. Thetubular strings are sometimes referred to in the art as “risers.”

These riser strings are immerged in the sea and are subject to movementscaused by sea currents and surface wave movements. Because of continuousand periodical movements of the sea, the tubular strings do not remainimmobile, but are subject to lateral movements of small magnitude whichcan produce deformations in certain parts of the tubular connections.These riser strings must withstand loads which induce fatigue stressesin the tubes and the tubular connections, in particular with respect tothe zone of the threaded connection. These stresses tend to causeruptures in the tube and/or connection in the vicinity of the thread andthere is a need to improve the fatigue resistance of the threadedconnections.

Some prior art patents, for example U.S. Pat. No. 7,780,202 and U.S.Pat. No. 6,609,735 disclose flank-to-flank (“FtF”) engagement typeconnections which are subject to fatigue, including riser connectors.

Other prior art conventional interference fit threaded connections(including API buttress-style thread forms), have profiles in which thethreads engage along only one thread flank upon make up. This type ofconnection must completely unload the contacting flank, undergo relativemovement between the pin and the coupling until the opposite flankscontact, and then transfer load to the newly contacting flank. Repeated,cyclical side loading and load transfers make these connection typesespecially susceptible to fatigue failures.

In flank-to-flank (FtF) threads, upon make up, contact is made betweenboth stabbing and load flanks Clearance exists between crests and roots.The thread is designed with the thread teeth of one member being widerthan the mating teeth of the other member (e.g., flank to flankinterference). Due to the inclination of the flanks, contact forces(normal to the surface of the flank) have the main component placed inan axial direction, pressing the material that forms the thread teeth.To achieve the flank to flank interference, contact forces work mainlyon the elasticity of the teeth. The elasticity of the teeth is very lowso high contact pressures are reached during make up. This explains whyFtF threads have high galling tendency during make up.

Additional drawbacks of FtF threads are present for very sloping anglesof the lead-in flank of the thread, measured compared to a perpendicularsurface to the pipe's axis. The compression action of the connection isunsatisfactory because this type of solution aids the onset of thephenomenon defined as “jump-in,” when the compression forces exceedcertain limits. Jump-in occurs when the male pipe segment slides intothe female segment, exceeding the resistance given by the threading ofthe two pieces. This phenomenon occurs more frequently the more inclinedthe angle of thread lead-in.

Other drawbacks of the FtF type of thread is that it is subject to highrisk of seizure of the joint with the consequent risk of not ensuringthe airtight seal of the fluids inside the tube. Due to the seizureeffect, torque varies greatly as the screwing operation (make up) of thejoint proceeds. This type of joint typically has more turns. Thisintroduces difficulties in making the joint and creates the possibilityof imprecision in applying the correct make up torque.

In Crest-to-Root (CtR) Threads (which are used in the threadedconnection of the present disclosure), upon make up, contact is madebetween a pair of mating flanks (load flanks for tension or stabbingflank for compression) and also contact between crest and roots. The CtRthread is designed with interference between crest and roots. In thiscase the main component of the contact forces (normal to the surface ofthe crest/root) are placed in a radial direction, and so theinterference is achieved taking advantage of the elasticity of a tubularbody by deforming geometrically the pipe. Only a minor part of theinterference is achieved by the elasticity of the thread teeth, socontact pressures achieved on the teeth are lower than in the case ofFtF threads, and so the galling tendency during make up is diminished.

The CtR design of the present disclosure has an optimum fatigueperformance and also a very low galling tendency during make up.Therefore, the presence of micro cracks (due to such galling) isminimized.

The present disclosure can be used in integral connections, threaded andcoupled connections and in big outside diameter (“OD”) threadedconnectors, for offshore and onshore applications. There are two majortypes of big OD threaded connectors used for production risers. Thefirst type is referred to in the art as a “welded” type; the pin and boxare machined separately from heavy-wall material and then welded to thepipe. In the second type, referred to in the art as“threaded-and-coupled” type, the pin is typically machined directly ontothe pipe ends. The box is machined into each end of a coupling that isused to join the pipe ends together.

Moreover, the design of the present disclosure can be combined withinternal and/or external/and or intermediate metal to metal sealconfigurations, internal and external elastomeric seals, intermediatemetal to metal seals and two step threads. For big diameter connectors,stabbing guides and anti-rotation devices can also be used together withthe thread profile of this disclosure.

SUMMARY

A threaded connection design having a double ellipse in the thread rootfor reducing fatigue stress is disclosed herein. In the design of thepresent disclosure the radius of the stress concentrator (located in thejoint between the root and the load flank) is increased using a doubleellipse configuration (curved surface having variable radius, not an arcof a circle which has a constant radius). This configuration allowsmaximizing the radius of the stress concentrator but also minimizes theloss of contact between load flanks, and also minimizes the section ofthe connection in which the “critical section” is diminished. Anotherbenefit of this profile is that the stress concentrator is put away fromthe contact points between pin and box so the tensional state on thestress concentrator is more beneficial to the fatigue behavior of thejoint. In the new design disclosed herein, maximized contact betweenload flanks and crest and roots is assured ( ) so the relative movementbetween parts of the connection is minimized. In general, the profile ofthe root surface in the present disclosure is composed by a linearportion and a curved portion having a double elliptical profile.

In particular, a design for a male or female threading, which isdisposed on an end of a tubular element, is disclosed. The male orfemale threading includes: a tapered root surface having a first angleof taper (β) measured from a longitudinal axis (aa) of the threading,said tapered root surface being joined tangentially at a first end by aconcave curved surface of a constant radius of curvature to a stabbingflank, said tapered root surface being joined at a second end by aconvex curved surface of constant radius of curvature to a root groove.The root groove extends from the tapered root surface to a load flank.

The root groove includes: a first portion comprising a first ellipticalsurface having a variable radius of curvature, said first ellipticalsurface being part of an ellipse, and said root groove further includinga second portion comprising a second elliptical surface having avariable radius of curvature, said second elliptical surface being partof a second ellipse, said second elliptical surface being joinedtangentially at a first end to the first elliptical surface at ajunction point that defines the bottom of the root groove; and saidsecond elliptical surface being joined tangentially at a second end tothe load flank. The bottom of the root groove is disposed in thesidewall of the tubular element below the level of the tapered rootsurface

The tapered root surface (101) includes a first angle of taper (β)measured between the tapered root surface 101 and a longitudinal axis(aa) of the of the threading. In some implementations the first angle oftaper (β) is 0 degrees, such that the tapered root surface (101, 301) isparallel to the axis of threading (aa). In other implementations thefirst angle of taper (β) greater than 0 but less than the measured valueof an angle measured between a stabbing flank 220 of the male threadingand the axis of threading (aa).

In some implementations an angle theta measured between the axis ofthreading (aa) and the longitudinal axis (dd) of the sidewall of thetubular element (11) is between 1.5 degrees and 12 degrees.

In the present disclosure, a major axis (cc) of the second ellipse isdisposed perpendicular to the load flank; and the major axis (bb) of thefirst ellipse is perpendicular to the major axis (cc) of the secondellipse. The major axis (bb) of the first ellipse is concurrent with aminor axis of the second ellipse.

In some implementations the first ellipse and the second ellipse are thesame size. For example, the first ellipse has a first predetermineddiameter (D1) along a major axis (bb), and a second predetermineddiameter (D2) along a minor axis; and wherein the second ellipse has apredetermined diameter (D3) along the major axis (cc) that is equal tothe diameter (D1) along the major axis (bb) of the first ellipse, andthe second ellipse has a second diameter (D4) along a minor axis that isequal to the diameter (D2) along the minor axis of the first ellipse.

In other implementations the ellipses may have differing shapes. Forexample, the first ellipse has a first predetermined diameter (D1) alonga major axis (bb), and a second predetermined diameter (D2) along aminor axis; and wherein the second ellipse has a predetermined diameter(D3) along a major axis (cc) that is equal to the diameter (D1) alongthe major axis (bb) of the first ellipse, and the second ellipse has asecond diameter (D4) along a minor axis that is greater than thediameter (D2) along the minor axis of the first ellipse. In otherimplementations, the second diameter (D4) along a minor axis of thesecond ellipse is greater than the diameter (D2) along the minor axis ofthe first ellipse, but the diameter of D1 may not necessarily be equalto the diameter of D3. In other implementations the second diameter (D4)along a minor axis is less than the diameter (D2) along the minor axisof the first ellipse. In other implementations the diameter (D3) alongthe major axis (cc) of the second ellipse is less than the diameter D1along the major axis (bb) of the first ellipse. In otherimplementations, the diameter (D3) along the major axis (cc) of thesecond ellipse may be greater than the diameter (D1) along the majoraxis (bb) of the first ellipse. It will be understood and is expresslydisclosed that any combination of one or more of the above ellipsediameter configurations may be combined in the implementation of thisinvention.

In some implementations, the load flank slopes away from the root grooveand an angle measured between the load flank and a line perpendicular toan axis of the threading (aa) is in the range of 0 to 5 degrees. This isreferred to in the art as a trapezoidal thread. In otherimplementations, the load flank slopes toward the root groove and anangle measured between the load flank and a line perpendicular to anaxis of the threading (aa) is in the range of 0 to −9 degrees. This isreferred to in the art as a hook thread.

The various implementations of the double ellipse root profile of thepresent invention may be used in a thread connection having a maletubular element including a tapered male threading having an axis oftaper (aa), and a female tubular element including a tapered femalethreading having an axis of taper (aa), said female threading cooperateswith the male threading when the threaded connection is made up. Theroot surface in at least one of the male threading and female threadingsincludes a tapered root surface having a first angle of taper (β)measured between the tapered root surface 101 and a longitudinal axis(aa) of the threading, said tapered root surface being joinedtangentially at a first end by a concave curved surface of a constantradius of curvature to a stabbing flank, said tapered root surface beingjoined at a second end by a convex curved surface of constant radius ofcurvature to a root groove. The root groove extends from the taperedroot surface to a load flank. The root groove includes: a first portioncomprising a first elliptical surface having a variable radius ofcurvature, said first elliptical surface being part of an ellipse, andsaid root groove further including a second portion comprising a secondelliptical surface having a variable radius of curvature, said secondelliptical surface being part of a second ellipse, said secondelliptical surface being joined tangentially at a first end to the firstelliptical surface at a junction point that defines the bottom of theroot groove; and said second elliptical surface being joinedtangentially at a second end to the load flank. The bottom of the rootgroove is disposed in the sidewall of the tubular element below thelevel of the tapered root surface.

A method is disclosed for cutting a tapered male or female threading ofthe double ellipse root profile of the present invention. The methodincludes: providing a tubular element; cutting a tapered male or femalethreading on an end of said tubular element wherein said tapered male orfemale threading includes a tapered root surface having a first angle oftaper (β) measured between the tapered root surface 101 and alongitudinal axis (aa) of the threading, said tapered root surface beingjoined tangentially at a first end by a concave curved surface of aconstant radius of curvature to a stabbing flank, said tapered rootsurface being joined at a second end by a convex curved surface ofconstant radius of curvature to a root groove. The root groove extendsfrom the tapered root surface to a load flank. The root groove includes:a first portion comprising a first elliptical surface having a variableradius of curvature, said first elliptical surface being part of anellipse, and said root groove further including a second portioncomprising a second elliptical surface having a variable radius ofcurvature, said second elliptical surface being part of a secondellipse, said second elliptical surface being joined tangentially at afirst end to the first elliptical surface at a junction point thatdefines the bottom of the root groove; and said second ellipticalsurface being joined tangentially at a second end to the load flank. Thebottom of the root groove is disposed in the sidewall of the tubularelement below the level of the tapered root surface.

The details of one or more implementations of the invention are setforth in the accompanying drawings and the description below. Otherfeatures, objects, and advantages of the invention will be apparent fromthe description and drawings, and from the claims.

DESCRIPTION OF DRAWINGS

FIG. 1 is a partial cross-section of a first implementation of athreaded connection design having a double ellipse in the thread rootfor reducing fatigue stress;

FIG. 1A is an enlarged portion of the cross-section of FIG. 1, whereinthe angle of thread taper is further enlarged for illustrative purposes;

FIG. 2 is a partial cross-section of a second implementation of athreaded connection design having a double ellipse in the thread rootfor reducing fatigue stress;

FIG. 2A is an enlarged portion of the cross-section of FIG. 2, whereinthe angle of thread taper is further enlarged for illustrative purposes;

FIG. 3 is a partial cross-section of a third implementation of athreaded connection design having a double ellipse in the thread rootfor reducing fatigue stress;

FIG. 3A is an enlarged portion of the cross-section of FIG. 3, whereinthe angle of thread taper is further enlarged for illustrative purposes;

FIGS. 4A to 4D are partial cross-sections illustrating different rootprofiles of a Crest-to-Root (“CtR”) thread;

FIG. 5 is a partial cross-section of a tubular connection with athreading profile of FIG. 1;

FIG. 6 is a partial cross-section of a tubular connection with athreading profile of FIG. 2;

FIG. 7 is a partial cross-section of a tubular connection with athreading profile of FIG. 3;

FIG. 8A is a graphical illustration of finite element analysis generateddata showing estimated cycles to fatigue failure for a standard priorart CtR thread;

FIG. 8B is a graphical illustration of finite element analysis generateddata showing estimated cycles to fatigue failure for a double ellipticalthread of the present disclosure;

FIG. 9A is a graphical illustration of finite element analysis generateddata showing stress distribution for a standard prior art CtR thread;and

FIG. 9B is a graphical illustration of finite element analysis generateddata showing stress distribution for a double elliptical thread of thepresent disclosure;

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

Referring to FIG. 1 where therein is illustrated a first implementationof a threaded connection design having a double ellipse in the threadroot for reducing fatigue stress. A tubular element has a male threading100 disposed on a pin end 12 of the tubular element 11. The malethreading 100 includes a tapered root surface 101. In the firstimplementation illustrated in FIG. 1, the tapered root surface 101 isparallel to the axis of threading (aa). The axis of threading (aa) formsan angle θ of approximately 2.4 degrees with a longitudinal axis (dd) ofthe wall of the tube 11. The range for theta in this implementation mayrange from about 1.5 degrees to 12 degrees, and more preferably from 1.5to 4.5 degrees. It will be understood that in this embodiment, since thetapered root surface 101 is parallel to the axis aa of the threading anangle β between the root tapered root surface 101 and the axis ofthreading (aa) will be equal to 0 degrees. However, in a modification ofthis embodiment, the angle β may have other values (e.g., see FIG. 2).

The tapered root surface 101 is joined tangentially at a first end by aconcave curved surface 102 of a constant radius of curvature to astabbing flank 120 and the tapered root surface 101 is joined at asecond end by a convex curved surface 104 of constant radius ofcurvature to a root groove 103. The root groove 103 extends from thetapered root surface 101 to a load flank 150.

The root groove 103 includes a first portion comprising a firstelliptical surface 106 having a variable radius of curvature. The firstelliptical surface 106 is part of an ellipse 107. The root groove 103further includes a second portion having a second elliptical surface 108with variable radius of curvature. The second elliptical surface is partof a second ellipse 110. The second elliptical surface 108 is joinedtangentially at a first end to the first elliptical surface 106 at ajunction point 109 that defines the bottom of the root groove 103. Thesecond elliptical surface is joined tangentially at a second end to theload flank 150.

The bottom of the groove 103 is placed below the level of the taperedroot surface 101.

The major axis (bb) of the first ellipse 107 is disposed perpendicularto the major axis (cc) of the second ellipse 110, and the major axis(bb) of the first ellipse 107 is concurrent with (aligned with andoverlaying) a minor axis of the second ellipse 110. This configurationensures that ellipses 107 and 110 join tangentially at the junctionpoint 109.

In the first implementation illustrated in FIG. 1, the major axis (cc)of the second ellipse 110 is disposed perpendicular to the load flank150. This configuration ensures that the second ellipse 110 is joinedtangentially to the load flank 150.

In the first implementation illustrated in FIG. 1, the first ellipse 107has a first predetermined diameter (D1) along the major axis (bb), and asecond predetermined diameter (D2) along a minor axis; and wherein thesecond ellipse 110 has a predetermined diameter (D3) along the majoraxis (cc) that is equal to the diameter (D1) along the major axis (bb)of the first ellipse 107, and the second ellipse 110 has a seconddiameter (D4) along a minor axis that is equal to the diameter (D2)along the minor axis of the first ellipse 107. In this configuration thefirst ellipse 107 and the second ellipse 110 are identically shaped.Alternatively, it will be understood that in the design of threading100, the first ellipse 107 and the second ellipse 110 may have differentrelative diameters. For example, the first ellipse 107 may be longer andnarrower than the implementation illustrated in FIG. 1 (e.g., theellipse may be shaped similar to the ellipse 207 illustrated in FIG. 2).

It will be understood that a female box connection may have the sameelements and profile as the male threading 100 illustrated and discussedabove.

Referring now to FIG. 5 wherein is illustrated a tubular connection 10having a first tube 11 with a male pin end 12 with the tapered malethreading 100 (as illustrated in FIG. 1) made up to a female box end 14of a second tube 13. The female box end 14 is illustrated with the samethreading profile 100 as the male threading 100. As discussedhereinafter it will be understood that the male threading and the femalethreading do not have to be identical and either the male threading orthe female threading may have modifications as discussed hereinafter.

In the first implementation illustrated in FIGS. 1, 1 A and 5, the loadflank 150 is sloped positively away from the root groove 103. (You willnote that FIG. 1A has the angle of the load flank 150 exaggerated forillustrative purposes.) Such a thread configuration is referred to inthe art as a trapezoidal thread. The angle of the load flank measuredwith a line perpendicular to the axis (aa) of the threading is generallyin the range of 0 to 5 degrees and more preferably from 1.5 to 5 degreesand preferably about 3 degrees. Moreover, angles from 0° (that is to sayload flank perpendicular to the axis (aa) of the threading can also beused. In addition, negative flank angles from −9° to 0 (e.g. see FIG. 3a) may also be used for variations of this embodiment. That is to say,the range angle of the load flank may range from −9° to 5° and apreferred range for this embodiment is 1.5° to 5° and the preferredvalue is 3°.

Referring to FIG. 2 where therein is illustrated a second implementationof a threaded connection design having a double ellipse in the threadroot for reducing fatigue stress. An axis of threading (aa) forms apreferred angle theta of approximately 2.4 degrees with a longitudinalaxis (dd) of the wall of the tube 21. The range for theta in thisimplementation may range from about 1.5 degrees to 12 degrees, and morepreferably from 1.5 to 4.5 degrees.

In the second implementation, a tapered threading 200 includes a taperedroot surface 201 disposed at an angle of taper (β) measured between theroot surface 201 and the axis of taper (aa) of the threading. The angleof taper (β) measured from the axis of taper (aa) of the threading isless than a measured angle between the stabbing flank (220) and the axisaa of the threading The tapered root surface 201 is joined tangentiallyat a first end by a concave curved surface 202 of a constant radius ofcurvature to a stabbing flank 220 and the tapered root surface 201 isjoined at a second end by a convex curved surface 204 of constant radiusof curvature to a root groove 203. The root groove 203 extends from thetapered root surface 201 to a load flank 250.

The root groove 203 includes a first portion having a first ellipticalsurface 206 with a variable radius of curvature. The first ellipticalsurface 206 is part of an ellipse 207. The root groove 203 furtherincludes a second portion having a second elliptical surface 208 with avariable radius of curvature. The second elliptical surface is part of asecond ellipse 210. The second elliptical surface 208 is joinedtangentially at a first end to the first elliptical surface 206 at ajunction point 209 that defines the bottom of the root groove 203. Thesecond elliptical surface is joined tangentially at a second end to theload flank 250. The bottom of the groove 203 is placed below the levelof the tapered root surface 201.

The major axis (bb) of the first ellipse 207 is disposed perpendicularto the major axis (cc) of the second ellipse 210, and the major axis(bb) of the first ellipse 207 is concurrent with (aligned with andoverlaying) a minor axis of the second ellipse 210. This configurationensures that ellipses 207 and 210 join tangentially at the junctionpoint 209.

In the second implementation illustrated in FIG. 2, the major axis (cc)of the second ellipse 210 is disposed perpendicular to the load flank250. This configuration ensures that the second ellipse 210 is joinedtangentially to the load flank 250.

In the second implementation, the first ellipse 207 has a firstpredetermined diameter (D1) along a major axis (bb), and a secondpredetermined diameter (D2) along a minor axis; and wherein the secondellipse 210 has a predetermined diameter (D3) along a major axis (cc)that is equal to the diameter (D1) along the major axis (bb) of thefirst ellipse 207, and the second ellipse 210 has a second diameter (D4)along a minor axis that is greater than the diameter (D2) along theminor axis of the first ellipse 207. Alternatively, it will beunderstood that in the design of threading 200, the first ellipse 207and the second ellipse 210 may have different relative diameters. Forexample, the second ellipse 210 may have a first diameter (D3) along amajor axis that may be greater than the diameter (D1) along the majoraxis of the first ellipse.

It will be understood that a female box connection may have the sameelements and profile as the male threading 200 illustrated and discussedabove.

Referring now to FIG. 6 wherein is illustrated a tubular connection 20having a first tube 21 with a male pin end 22 with the tapered malethreading 200 (as illustrated in FIG. 2) made up to a female box end 24of a second tube 23. The female box end 24 is illustrated with amodified threading profile 100 (as illustrated in FIG. 3). It will beunderstood that the male threading and the female threading do not haveto be identical as illustrated in FIG. 6, as long as the surfaces aredesigned to mate properly. It will also be understood that the malethreading and female threading may be identical as previously discussedherein with regard to FIGS. 1 and 5.

In the second implementation (see FIGS. 2, 2A and 6), the load flank 250is sloped positively away from the root groove 203. (You will note thatFIG. 2A has the angle of the load flank 150 exaggerated for illustrativepurposes). Such a thread configuration is referred to in the art as atrapezoidal thread. The angle of the load flank 250 measured between aline perpendicular to the pipe axis (aa) of the threading is generallyin the range of 0 to 5 degrees and more preferably from 1.5 to 5 degreesand preferably about 3 degrees. In variations of this embodiment andangle of 0° (that is to say load flank perpendicular to the axis (aa)can also be used. In addition, negative flank angles from −9° to 0 (e.g.see FIG. 3) may also be used for this embodiment. That is to say, theangle of the load flank may range from −9° to 5° with a preferred rangefor this embodiment of 1.5° to 5° and the preferred value being 3°.

Referring to FIG. 3 where therein is illustrated a third implementationof a threaded connection design 300 having a double ellipse in thethread root for reducing fatigue stress. The tapered male threading 300includes a tapered root surface 301. The axis of the threading (aa)forms a preferred angle theta with the longitudinal axis of the tube(dd) of approximately 8 degrees. The range for theta in thisimplementation may range from about 1.5° to 12 degrees and morepreferably from 4.5 degrees to 12 degrees.

In the third implementation illustrated in FIG. 3, the tapered rootsurface 301 is parallel to the axis of threading (aa) as in theimplementation of FIG. 1. It will be understood that in this embodiment,since the tapered root surface 301 is parallel to the axis aa of thethreading an angle β between the root tapered root surface 301 and theaxis of threading (aa) will be equal to 0 degrees. However, in amodification of this embodiment, the angle β may have other values (e.g.see FIG. 2).

The tapered root surface 301 is joined tangentially at a first end by aconcave curved surface 302 of a constant radius of curvature to astabbing flank 320 and the tapered root surface 301 is joined at asecond end by a convex curved surface 304 of constant radius ofcurvature to a root groove 303. The root groove 303 extends from thetapered root surface 301 to a load flank 350.

The root groove 303 includes a first portion having a first ellipticalsurface 306 with a variable radius of curvature. The first ellipticalsurface 306 being part of an ellipse 307. The second elliptical surfaceis part of a second ellipse 310. The root groove 303 further includes asecond portion having a second elliptical surface 308 with a variableradius of curvature. The second elliptical surface 308 is joinedtangentially at a first end to the first elliptical surface 306 at ajunction point 309 that defines the bottom of the root groove 303. Thesecond elliptical surface is joined tangentially at a second end to theload flank 350. The bottom of the groove 303 is placed below the levelof the tapered root surface 301.

In the third implementation illustrated in FIG. 3, the first ellipse 307has a first predetermined diameter (D1) along the major axis (bb), and asecond predetermined diameter (D2) along a minor axis; and wherein thesecond ellipse 310 has a predetermined diameter (D3) along the majoraxis (cc) that is equal to the diameter (D1) along the major axis (bb)of the first ellipse 307, and the second ellipse 310 has a seconddiameter (D4) along a minor axis that is equal to the diameter (D2)along the minor axis of the first ellipse 307. Alternatively, it will beunderstood that in the design of threading 300, the first ellipse 307and the second ellipse 110 may have different relative diameters. Forexample, the first ellipse 307 may be longer and narrower than theimplementation illustrated in FIG. 3 (e.g., the ellipse may be shapedsimilar to the ellipse 207 illustrated in FIG. 2).

The major axis (bb) of the first ellipse 307 is disposed perpendicularto the major axis (cc) of the second ellipse 310, and the major axis(bb) of the first ellipse 307 is concurrent with (aligned with andoverlaying) a minor axis of the second ellipse 310. This configurationensures that ellipses 307 and 310 join tangentially at the junctionpoint 309.

In the third implementation illustrated in FIG. 3, the major axis (cc)of the second ellipse 310 is disposed perpendicular to the load flank350. This configuration ensures that the second ellipse 310 is joinedtangentially to the load flank 350. All orientations of other axis aredefined with respect to axis cc of the second ellipse 310.

It will be understood that a female box connection may have the sameelements and profile as the male threading 300 illustrated and discussedabove.

Referring now to FIG. 7 wherein is illustrated a tubular connection 30having a first tube 31 with a male pin end 32 with the tapered malethreading 300 (as illustrated in FIG. 3) made up to a female box end 34of a second tube 33. The female box end 34 is illustrated with the samethreading profile 300 as the male threading 300. As discussed previouslyherein with regard to FIGS. 2 and 6, it will be understood that the malethreading and the female threading do not have to be identical andeither the male threading or the female threading may have modificationsas long as the profiles mate together.

In the third implementation illustrated in FIGS. 3, 3 A and 7, the loadflank 350 is sloped toward the root groove 303. (You will note that FIG.3A has the angle of the load flank 350 exaggerated for illustrativepurposes.) Such a thread configuration is referred to in the art as ahook thread. The angle of the load flank measured with a lineperpendicular to the axis (aa) of the threading is generally in therange of −9 to 0 degrees and more preferably from −9 to −1.5 degrees andpreferably about −3 degrees. Moreover, angles from 0° (that is to sayload flank perpendicular to the axis (aa) can also be used. In addition,positive flank angles from 0° to 5 degrees (e.g. see FIG. 1a ) may alsobe used for variations of this embodiment. That is to say, the rangeangle of the load flank may range from −9° to 5, a more preferably theangle may range between −9 to −1.5 and a preferred value for thisembodiment is −3°.

The present disclosure also includes a method of cutting a male orfemale threading 100, 200, 300 on an end of a tubular element. Themethod includes: providing a tubular element 11, 21, 31, 13, 23, 33;cutting a tapered male or female threading on a respective pin end 12,22, 32 or box end 14, 24, 34 of the tubular element wherein the taperedthreading includes a root surface 101, 201, 301. The tapered rootsurface 101, 201, 301 is joined tangentially at a first end by a concavecurved surface 102, 202, 302 of a constant radius of curvature to astabbing flank 120, 220, 320. The tapered root surface 101, 201, 301 isjoined at a second end by a convex curved surface 104 of constant radiusof curvature to a root groove 103. The root groove 103, 203, 303 extendsfrom the tapered root surface 101, 201, 301 to a load flank 150, 250,350. The root groove 103, 203, 303 includes: a first portion comprisinga first elliptical surface 106, 206, 306 having a variable radius ofcurvature, said first elliptical surface 106, 206, 306 being part of anellipse 107, 207, 307, and the root groove 103, 203, 303 furtherincluding a second portion comprising a second elliptical surface 108,208, 308 having variable radius of curvature, said second ellipticalsurface being a part of the second ellipse 110, 210, 310. The secondelliptical surface 108, 208, 308 is joined tangentially at a first endto the first elliptical surface 106, 206, 306 at a junction point thatdefines the bottom of the groove 109, 209, 309. The second ellipticalsurface is joined tangentially at a second end to the load flank 105,205, 305. The second elliptical surface has its major axis (cc)perpendicular to the load flank 150, 250, 350. The major axis bb isperpendicular to the major axis cc. Orientation of axis is definedhaving in mind that cc should be perpendicular to the load flank andthat bb and cc should be one perpendicular to the other.

Advantages of Present Invention

The root profile design of the present disclosure improves fatigueresistance of the threaded connection by a combined action of severalfeatures which manifest themselves at the end of the make up operationof the connection:

a) provision of large radial loads (“hoop loads”), as a function ofroot-to-crest interference. The large hoop loads improve fatigueresistance;

b) provision of large shoulder loads that improve fatigue resistance;and

c) provision of an lengthened radius Rb (of the arc of the curve theconnects the root to the flank) lowers stress concentration in thethread roots.

The present design configuration of two ellipses allows maximization ofthe radius of the stress concentrator in the joint between the loadflank 150, 250, 350 and the root surface 101, 201, 301, so the effect ofthe stress concentrator on the fatigue performance of the joint isminimized. Moreover, the effective contact between mating load flanks ofthe male and female element 12 and 14 of the connection 10 is alsomaximized and hence efficiency of the connection is also maximized.

FIGS. 4A, 4B, 4C and 4D illustrate problems and benefits of incrementalchange in design configuration from the prior art standard CtR design ofFIG. 4A to an exemplary root design of the present disclosure asillustrated in FIG. 4D. In FIGS. 4A to 4D, Rb is the radius of the arcconnecting the root of the male thread to the load flank of the malethread. Ri is the radius of the arc connecting the thread crest and theload flank of the female thread. See FIG. 4A wherein the Rb and the Riare equal.

Referring to FIG. 4A, wherein is illustrated a full load flank contact.Problem: contact pressures over the stress concentrator and low stressconcentrator radius (Rb). Benefit: High tension efficiency due tomaximized load flank contact L1.

Referring to FIG. 4B wherein is illustrated a modified CtR profile(similar to prior art design of US 20110042946 A1). Benefit: The radiusRi is enlarged to avoid contact points over the stress concentrator.Problem: The stress state near the stress concentrator is highlyaffected by contact stresses and remote stresses. Another problem ofthis configuration is the low stress concentrator radius (Rb). Thisconfiguration has the same Rb as in FIG. 4A.

Referring to FIG. 4C to maximize the stress concentrator radius Rb,there is the limit of (Rb), because it is important to avoid full loadflank contact. Moreover, when increasing Rb the effect of contactstresses in the stress state around the stress concentrator becomesbigger because points A and C are closer to B.

Referring to FIG. 4D wherein the stress concentrator radius (RI) of themale thread has been enlarged to maximize load flank contact and crestto root contact. Moreover, the stress state in the stress concentratoris less influenced by contact stresses and is only a function of remotestresses, due to the fact that contact points A and C are spaced fartheraway from the stress concentrator. With this geometry, contact surfaceL1 is restored but without contact in the stress concentrator.

Referring to FIG. 4B (a prior art design similar to US 2011 0042946 A1)and FIG. 4D (an implementation of the present root design), anotherbenefit of using the double elliptical groove as illustrated in FIGS. 1,2 and 3 of the present disclosure is that the stress state around thestress concentrator (KT) is less affected by the components of stressesdue to contact points (σ_(A)+σ_(C)), and so values of stresses are lowerthan the ones obtained for a joint without a groove and only affected byremote stresses (σ_(B)).

In some prior art CtR threads (see FIG. 4B), the stress state around thestress concentrator KT is a function of contact stresses (σ_(A)+σ_(C))and remotes stresses (σ_(B)):σ_(KT)=σ_(A)+σ_(B)+σ_(C)

However, in the joint of the present disclosure (see FIG. 4D), contactpoints A and C are far away from the stress concentrator, so the stressstate around the stress concentrator KT is a function only of theremotes stresses (σ_(B)):σ_(KT)=σ_(B)

It is important to note that the choice of ellipses to form the grooveis based on the fact that the ellipses are functions that allow joiningtwo perpendicular surfaces with a curved surface that has a radius thatvaries from point to point. Therefore, the radiuses can be maximized andminimized. For example, an arc of circle having the same radius as theradius of the ellipse in the KT will remove all possibility of contactbetween load flanks (see FIGS. 1 to 3).

The use of a second ellipse to go from the load flank to the KT is usedto maximize the radius of the KT, then the design switches to the firstellipse to quickly restore crest to root contact. This design provides aminimal removal of crest to root contact surface. Therefore, contactpressures are maintained low (see FIGS. 1 to 3).

To enhance the effect of the first ellipse, it can be narrowed asillustrated in the second implementation of the present disclosure (seeFIG. 2).

Additionally increasing the taper of the tapered portion of the rootsurface as illustrated in the second implementation (FIG. 2), thecontact surface between crest and root is enlarged and so contactpressures are minimized and galling is minimized. The contact length atcrest/root is approximately double in the second implementation ascompared to the design illustrated in the first implementation. Thisdesign minimizes galling. Additionally, positive (major than 0) angle oftaper (β) measured from the axis of taper (aa) of the threading helps tomaintain the thread locked. (β) angle is also useful in enlarging thecrest/root contact surface and at the same time provides for additionalroom for the groove for stress reduction at the pin root (see FIG. 2).

Referring now to FIGS. 8A, 8B, 9A and 9B, wherein finite elementanalysis has been used to generate data comparing parameters for astandard Crest to Root (CtR) thread (as illustrated in FIG. 4A) to theexemplary double elliptical design of the present disclosure (asillustrated in FIG. 4D). In FIG. 8A the cycles to fatigue failure isillustrated for the standard CtR thread design. In FIG. 8B the cycles tofatigue failure are illustrated for the double elliptical design of thepresent disclosure. It can be seen in FIGS. 8A and 8B how the doubleelliptical design of the present invention directly impacts on thenumber of cycles to failure in the zone where the stress concentrator isplaced. The first layer of material (in the area of the stressconcentrator, that is to say the joint between load flank and rootsurface) in the standard CtR design is the one having less number ofcycles 1.120×10⁺³ to fatigue failure (FIG. 8A), while dotted area (areanear the stress concentrator) in the double elliptic profile (FIG. 8B)is the one having less number of cycles 1.0×10⁺⁴. It can be seen thatthe fatigue life of the component is increased with the doubleelliptical design of the present invention.

Referring to FIGS. 9A and 9B, the stress distribution and representativevon Misses values for the standard CtR thread is illustrated in FIG. 9Aand the double elliptical thread profile of the present disclosure isillustrated in FIG. 9B. It can be seen that in FIG. 9A (prior art CtRdesign), high values of von Misses stress exist around the stressconcentrator and near the contact points between the male and femalethread near the stress concentrator. However, FIG. 9B, (the doubleelliptical thread profile of the present inventions) demonstrates alower level of stress values and a more uniform distribution of stressnear the stress concentrator. The contact points between the male andfemale members are desirably spaced apart from the stress concentratorand therefore not contributing to the stress state of the area near thestress concentrator.

A number of embodiments of the invention have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the invention.Accordingly, other embodiments are within the scope of the followingclaims.

What is claimed is:
 1. A method of cutting a tapered male threading onan end of a tubular element, said method comprising: providing a tubularelement; cutting a tapered male threading on an end of said tubularelement wherein said tapered male threading comprises: a tapered rootsurface having a first angle of taper (β) measured between the taperedroot surface and a longitudinal axis (aa) of threading, said taperedroot surface being joined tangentially at a first end by a concavecurved surface of a constant radius of curvature to a stabbing flank,said tapered root surface being joined at a second end by a convexcurved surface of constant radius of curvature to a root groove; saidroot groove extending from the tapered root surface to a load flank,said root groove including: a first portion comprising a firstelliptical surface having a variable radius of curvature, said firstelliptical surface being part of an ellipse, and said root groovefurther including a second portion comprising a second ellipticalsurface having a variable radius of curvature, said second ellipticalsurface being part of a second ellipse, said second elliptical surfacebeing joined tangentially at a first end to the first ellipticalsurface, and said second elliptical surface being joined tangentially ata second end to the load flank.
 2. The method of cutting a tapered malethreading of claim 1 wherein the first angle of taper (β) is 0 degrees,such that the tapered root surface is parallel to the axis of threading(aa).
 3. The method of cutting a tapered male threading of claim 1wherein the first angle of taper (β) is less than the measured value ofan angle measured between a stabbing flank of the male threading and theaxis of threading (aa).
 4. The method of cutting a tapered malethreading of claim 1 wherein an angle theta measured between the axis ofthreading (aa) and the longitudinal axis (dd) of the sidewall of thetubular element is between 1.5 degrees and 12 degrees.
 5. The method ofcutting a tapered male threading of claim 1 wherein a major axis (cc) ofthe second ellipse is disposed perpendicular to the load flank.
 6. Themethod of cutting a tapered male threading of claim 1 wherein a majoraxis (bb) of the first ellipse is perpendicular to a major axis (cc) ofthe second ellipse.
 7. The method of cutting a tapered male threading ofclaim 1 wherein a major axis (bb) of the first ellipse is aligned with aminor axis of the second ellipse.
 8. The method of cutting a taperedmale threading of claim 1 wherein the first ellipse has a firstpredetermined diameter (D1) along a major axis (bb), and a secondpredetermined diameter (D2) along a minor axis; and wherein the secondellipse has a predetermined diameter (D3) along a major axis (cc) thatis equal to the diameter (D1) along the major axis (bb) of the firstellipse, and the second ellipse has a second diameter (D4) along a minoraxis that is equal to the diameter (D2) along the minor axis of thefirst ellipse.
 9. The method of cutting a tapered male threading ofclaim 1 wherein the first ellipse has a first predetermined diameter(D1) along a major axis (bb), and a second predetermined diameter (D2)along a minor axis; and wherein the second ellipse has a predetermineddiameter (D3) along a major axis (cc) that is equal to the diameter (D1)along the major axis (bb) of the first ellipse, and the second ellipsehas a second diameter (D4) along a minor axis that is greater than thediameter (D2) along the minor axis of the first ellipse.
 10. The methodof cutting a tapered male threading of claim 1 wherein the first ellipsehas a first predetermined diameter (D1) along a major axis (bb), and asecond predetermined diameter (D2) along a minor axis; and wherein thesecond ellipse has a predetermined diameter (D3) along a major axis (cc)and has a second diameter (D4) along a minor axis that is greater thanthe diameter (D2) along the minor axis of the first ellipse.
 11. Themethod of cutting a tapered male threading of claim 1 wherein the firstellipse has a first predetermined diameter (D1) along a major axis (bb),and a second predetermined diameter (D2) along a minor axis; and whereinthe second ellipse has a predetermined diameter (D3) along a major axis(cc) and has a second diameter (D4) along a minor axis that is less thanthe diameter (D2) along the minor axis of the first ellipse.
 12. Themethod of cutting a tapered male threading of claim 1 wherein the firstellipse has a first predetermined diameter (D1) along a major axis (bb),and a second predetermined diameter (D2) along a minor axis; and whereinthe second ellipse has a predetermined diameter (D3) along a major axis(cc) and has a second diameter (D4) along a minor axis; and wherein thediameter (D3) along the major axis (cc) of the second ellipse is lessthan the diameter D1 along the major axis (bb) of the first ellipse. 13.The method of cutting a tapered male threading of claim 1 wherein thefirst ellipse has a first predetermined diameter (D1) along a major axis(bb), and a second predetermined diameter (D2) along a minor axis; andwherein the second ellipse has a predetermined diameter (D3) along amajor axis (cc) and has a second diameter (D4) along a minor axis; andwherein the diameter (D3) along the major axis (cc) of the secondellipse is greater than the diameter (D1) along the major axis (bb) ofthe first ellipse.
 14. The method of cutting a tapered male threading ofclaim 1 wherein the load flank is disposed in relation to an anglemeasured between the load flank and a line perpendicular to an axis ofthe threading (aa), wherein said angle ranges from −9 to 5 degrees. 15.The method of cutting a tapered male threading of claim 1 wherein thesecond elliptical surface is joined tangentially at a first end to thefirst elliptical surface at a junction point that defines the bottom ofthe root groove.
 16. A method of cutting a tapered female threading onan end of a tubular element, said method comprising: providing a tubularelement; cutting a tapered female threading on an end of said tubularelement wherein said tapered female threading comprises: a tapered rootsurface having a first angle of taper (β) measured between the taperedroot surface and a longitudinal axis (aa) threading, said tapered rootsurface being joined tangentially at a first end by a concave curvedsurface of a constant radius of curvature to a stabbing flank, saidtapered root surface being joined at a second end by a convex curvedsurface of constant radius of curvature to a root groove; said rootgroove extending from the tapered root surface to a load flank, saidroot groove including: a first portion comprising a first ellipticalsurface having a variable radius of curvature, said first ellipticalsurface being part of an ellipse, and said root groove further includinga second portion comprising a second elliptical surface having avariable radius of curvature, said second elliptical surface being partof a second ellipse, said second elliptical surface being joinedtangentially at a first end to the first elliptical surface, and saidsecond elliptical surface being joined tangentially at a second end tothe load flank.
 17. The method of cutting a tapered female threading ofclaim 16 wherein the first angle of taper (β) is 0 degrees, such thatthe tapered root surface is parallel to the axis of threading (aa). 18.The method of cutting a tapered female threading of claim 16 wherein thefirst angle of taper (β) is less than the measured value of an anglemeasured between a stabbing flank of the male threading and the axis ofthreading (aa).
 19. The method of cutting a tapered female threading ofclaim 16 wherein an angle theta measured between the axis of threading(aa) and the longitudinal axis (dd) of the sidewall of the tubularelement is between 1.5 degrees and 12 degrees.
 20. The method of cuttinga tapered female threading of claim 16 wherein a major axis (cc) of thesecond ellipse is disposed perpendicular to the load flank.
 21. Themethod of cutting a tapered female threading of claim 16 wherein a majoraxis (bb) of the first ellipse is perpendicular to a major axis (cc) ofthe second ellipse.
 22. The method of cutting a tapered female threadingof claim 16 wherein a major axis (bb) of the first ellipse is alignedwith a minor axis of the second ellipse.
 23. The method of cutting atapered female threading of claim 16 wherein the first ellipse has afirst predetermined diameter (D1) along a major axis (bb), and a secondpredetermined diameter (D2) along a minor axis; and wherein the secondellipse has a predetermined diameter (D3) along a major axis (cc) thatis equal to the diameter (D1) along the major axis (bb) of the firstellipse, and the second ellipse has a second diameter (D4) along a minoraxis that is equal to the diameter (D2) along the minor axis of thefirst ellipse.
 24. The method of cutting a tapered female threading ofclaim 16 wherein the first ellipse has a first predetermined diameter(D1) along a major axis (bb), and a second predetermined diameter (D2)along a minor axis; and wherein the second ellipse has a predetermineddiameter (D3) along a major axis (cc) that is equal to the diameter (D1)along the major axis (bb) of the first ellipse, and the second ellipsehas a second diameter (D4) along a minor axis that is greater than thediameter (D2) along the minor axis of the first ellipse.
 25. The methodof cutting a tapered female threading of claim 16 wherein the firstellipse has a first predetermined diameter (D1) along a major axis (bb),and a second predetermined diameter (D2) along a minor axis; and whereinthe second ellipse has a predetermined diameter (D3) along a major axis(cc) and has a second diameter (D4) along a minor axis that is greaterthan the diameter (D2) along the minor axis of the first ellipse. 26.The method of cutting a tapered female threading of claim 16 wherein thefirst ellipse has a first predetermined diameter (D1) along a major axis(bb), and a second predetermined diameter (D2) along a minor axis; andwherein the second ellipse has a predetermined diameter (D3) along amajor axis (cc) and has a second diameter (D4) along a minor axis thatis less than the diameter (D2) along the minor axis of the firstellipse.
 27. The method of cutting a tapered female threading of claim16 wherein the first ellipse has a first predetermined diameter (D1)along a major axis (bb), and a second predetermined diameter (D2) alonga minor axis; and wherein the second ellipse has a predetermineddiameter (D3) along a major axis (cc) and has a second diameter (D4)along a minor axis; and wherein the diameter (D3) along the major axis(cc) of the second ellipse is less than the diameter D1 along the majoraxis (bb) of the first ellipse.
 28. The method of cutting a taperedfemale threading of claim 16 wherein the first ellipse has a firstpredetermined diameter (D1) along a major axis (bb), and a secondpredetermined diameter (D2) along a minor axis; and wherein the secondellipse has a predetermined diameter (D3) along a major axis (cc) andhas a second diameter (D4) along a minor axis; and wherein the diameter(D3) along the major axis (cc) of the second ellipse is greater than thediameter (D1) along the major axis (bb) of the first ellipse.
 29. Themethod of cutting a tapered female threading of claim 16 wherein theload flank is disposed in relation to an angle measured between the loadflank and a line perpendicular to an axis of the threading (aa), whereinsaid angle ranges from −9 to 5 degrees.
 30. The method of cutting atapered female threading of claim 16 wherein the second ellipticalsurface is joined tangentially at a first end to the first ellipticalsurface at a junction point that defines the bottom of the root groove.